Cuomo's busy schedule raises questions about his political intentions. Is he running for president or just being a good governor?

The governor is busy being governor. Back from week-long trip to the Soviet Union, Gov. Mario Cuomo (D) answers questions in the gym at Eugenio Maria de Hostos Community College in the south Bronx.

``What is the state doing about the devastating problem of domestic violence?'' asks a woman from a crisis-intervention program.

``Can't the state offer more aid to the visually impaired and the disabled?'' queries a blind student at Hostos College.

The drug problem, particularly crack, continues to grow, another Bronx resident says. A black businessman thanks the governor for his support of minority- and woman-owned businesses and wants to know more about an ``opportunity zone'' created in the area.

The governor fields the questions well, talks personally with each questioner, and generally seems to have fun. But some of the loudest applause comes when State Assemblyman Jose Serrano tells Governor Cuomo, ``We're with you here, in Albany ... and anywhere else you want to be!''

Cuomo himself steadfastly denies that he is running for president. ``I have no great desire to prove that I could to get to the top of the heap,'' he said yesterday on CBS-TV's ``Face the Nation.''

His campaign war chest has remained stable at around $3.6 million for the past year. His staff continues to be mainly New York talent. But he continues to make keynote speeches around the country. His trip to the Soviet Union attracted a great deal of media attention.

To some, Cuomo is the official noncandidate of the 1988 presidential election. Certainly among constituents at the Bronx vox populi meeting there is support for a Cuomo presidential bid. But other observers say Cuomo is simply eager to broaden his knowledge of issues that effect his state and the nation.

In a poll to be released today by the Marist College Institute for Public Opinion, New York voters continue to give Cuomo high approval ratings. Institute director Lee Miringoff says Cuomo is able to expand his schedule, his background, and his expertise without voters seeing it as a liability in running the state.

But, interestingly, though an increasing number of New Yorkers say they believe Cuomo should run for the Democratic nomination, there is also an increasing number who think that he will not join the fray, Dr. Miringoff says.

Some voters in the south Bronx, a national symbol of urban blight that has been toured by both Presidents Carter and Reagan, express that wistfulness.

``He would make a terrific president,'' says Bedelia Garcia, a student at Hostos. ``He's not the kind that would mess himself up.''

``I wish he'd run for president,'' says Adrian Benitez, an instructor at Hostos. ``He would bring wisdom, a sense of balance between values and pressures.''

Others are not as keen.

``I don't trust the Democrats,'' says Paul Wayne, a student. ``They make too many promises and they do not fulfill them. The Democrats believe in giving to the minorities. We do not want to be given. We cannot live on welfare all the time. We want to do things for ourselves.''

Political observers note that Cuomo appears to enjoy the give-and-take sessions, whether it be with Soviet leaders or South Bronx activists, much more than he does actual compaigning.

``He doesn't enjoy running as much as being an office holder,'' Miringoff says.

Others express a weariness over the continual speculation of whether Cuomo will run. ``If it was December 1988, he wouldn't be viewed as a noncandidate, but as a national leader,'' says Mark Pearl, director of Americans for Democratic Action. ``He recognizes the need for and importance of a national spokesman on the American political scene. Unfortunately you can't do that without people saying you are a candidate.''

``Mechanically, the door is still open for Cuomo,'' says Will Feltus, vice-president of Market Opinion Research, a polling firm that works with Republican candidates. In light of what is happening among current Democratic candidates, ``there are a lot of Democrats who would like to see Cuomo darken their door.''

But, Mr. Feltus says, whatever kept Cuomo from running is still an important factor. It was not, he says, that the governor was afraid of Gary Hart, Joseph Biden, or Michael Dukakis. Cuomo is also denying rumors that he is afraid to run because it could expose misdeeds in his family's past.

His efforts to become a visionary, important voice within the Democratic Party - through his growing interest in international issues, for example - may force his hand or spur him to make a job change, Mr. Pearl says. But it might also be preparation for a campaign for the presidency in 1992.

Miringoff notes that Cuomo often shows a good sixth sense about voter concerns, citing both state tax cuts and his trip to the Soviet Union. Marist polls show that arms control is a top concern of voters here, and, Cuomo commented while in Moscow that the declared contenders should be talking about ending the arms race and peace or else ``they're missing the boat.''

Monitor intern Mxolisi Mgxashe assisted in reporting this article.